Shape

15 Answer Number Two—Three More Ways to Look at It That Tell a Story
that I’ve already invoked a few times. It gives a pretty good idea of what I hope to accomplish.
The formula translates easily into a rule of the form
see x fi do y
where the variables x and y can have all sorts of things as values. But for most of my
purposes, it’s enough for x and y to be shapes. For example, the rule
that rotates a triangle turns the shape
into the shape
in a single step with two stages. I see the triangle
and trace it out. It’s part of the shape
because its sides are embedded in the lines of the shape. And then I erase the triangle
and draw another one
I’m going to be saying a lot about how to use rules like this automatically, so that seeing
parts and replacing them by erasing lines and drawing more go together in a mechanical
process in which the details are all worked out. And I’m going to show that
being mechanical in this way and being creative aren’t opposed when you calculate
with shapes. It’s mostly a question of getting embedding right, so that you’re reasoning
with your eyes. My rules let you see. But first, I need to say a little more about rules as